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Comparison of the three presented noise estimators for different colors of noise. We show the original Donoho noise estimator (solid black), a wavelet estimator that takes into account all wavelet scales (Donoho-FULL, short-dashed red), and our adapted Donoho estimator (long-dashed blue). The β value, representing the power of the spectral density, is varied from −2 (Brownian noise) to 2, where 2 is violet noise (1 would be blue noise). Each point represents the estimated noise level of a one thousand point randomly generated time series of the specified power. The spread indicates the standard deviation of the estimator from one hundred trial runs. While the classical Donoho estimator overestimates all noise for β > 0, but using all wavelet components underestimates the noise of the same data, the adapted Donoho estimator provides a better estimate.
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